(eng): Any prescriptive theory of decision-making (DM) has to cope with the common DM agents’ inability to fully specify their preferences dependent on several attributes. The paper provides the needed preference completion and quantification for fully probabilistic design (FPD) of DM strategies. FPD (covering the usual Bayesian DM) probabilistically models the agent’s environment and quantifies its preferences via an ideal probabilistic model of the closed DM loop. The probability density (pd) models (closed-loop) behaviour, a collection of involved random variables. Its ideal twin is high on desired behaviours, small on undesired and zero on forbidden ones. The FPD-optimal strategy minimises the Kullback-Leibler divergence (KLD) of the closed-loop modelling pd to the ideal twin. The exposed preference quantification chooses the optimal ideal pd from the set of pds compatible with partially-specified agent’s preferences. The optimal ideal pd minimises the KLD minima reached by the optimal strategies for respective imminent ideal pds. This preference-focused twin of the minimum KLD principle was applied to special sets of ideal pds. The paper extends them towards exploration and balancing contradictory wishes on states and actions.